Problem: The measures of the angles of a triangle are in a ratio of $3:5:7$. What is the degree measure of the largest angle?
Answer: Let $3k$ be the measure of the smallest angle. Then the other two angles measure $5k$ and $7k$. Since the interior angles of a triangle sum to 180 degrees, we have $3k+5k+7k=180^\circ$, which implies $k=180^\circ/15=12^\circ$. The largest angle is $7k=7(12^\circ)=\boxed{84}$ degrees.